Localized states in the continuum in low-dimensional systems

It is shown in this paper that for open systems, states which are localized in space, discrete in energy, and embedded in the continuum of extended states, can be sustained by low-dimensional and channeled leads. These states have an origin different from that of analogous states discussed by J. von Neumann and E. Wigner [Phys. Z., vol. 30, 465 (1929)]. A few representative systems are discussed. These states cause, for example, infinitely sharp Fano resonance in transport when they are marginally destroyed.